Player model sometimes leaves horse while riding up blocks

The bug

When riding a horse, the player sometimes appears to travel forwards while the horse remains stationary. The frequency of this occurrence increases with the speed of the horse.

How to reproduce

The following reproduction steps were provided by Brain81505 in this comment.

1. Summon a horse, it could be anywhere but I think the easiest is to summon in the End.
2. Run this command if testing in 1.21.1:

   /execute as @n[type=horse] run attribute @s minecraft:generic.movement_speed base set 1

   Or this command if testing in 1.21.2+:

   /execute as @n[type=horse] run attribute @s minecraft:movement_speed base set 1

   This makes the horse run very fast.

3. Ride the horse, run and jump around randomly until the issue occurs.